Precision of the Anchor Influences the Amount of Adjustment Chris Janiszewski and Dan Uy

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1 PSYCHOLOGICAL SCIENCE Research Article Precision of the Anchor Influences the Amount of Adjustment Chris Janiszewski and Dan Uy University of Florida ABSTRACT The ing-and-adjustment heuristic has been used to account for a wide variety of numerical judgments. Five studies show that adjustment away from a numerical is smaller if the is precise than if it is rounded. Evidence suggests that precise s, compared with rounded s, are represented on a subjective scale with a finer resolution. If adjustment consists of a series of iterative mental movements along a subjective scale, then an adjustment from a precise should result in a smaller overall correction than an adjustment from a rounded. The ing-and-adjustment heuristic (Tversky & Kahneman, 1974) has been used to account for a wide variety of numerical judgments, including appraisals of home values (Northcraft & Neale, 1987), estimates of risk and uncertainty (Wright & Anderson, 1989), and estimates of future performance (Switzer & Sniezek, 1991). In all these cases, the explanation rests on the claim that a numerical judgment can be influenced by the prior consideration of a numerical (i.e., referent). For example, Northcraft and Neale (1987) asked real estate agents to estimate the appraised value of a home. Agents who received an information packet that included a higher list price estimated a higher appraisal value. Northcraft and Neale proposed that the agents started the judgment process by rejecting the list price as an accurate estimate and then adjusted downward until they reached a plausible estimate. Adjustments tend to be insufficient, so the final appraisal values were biased in the direction of the initial value. Address correspondence to Chris Janiszewski, Warrington College of Business Administration, University of Florida, P.O. Box , Gainesville, FL , chris.janiszewski@cba.ufl.edu. Two fundamental questions concerning numerical judgments are, when do people adjust, and what factors influence the amount of adjustment? With respect to the first question, recent evidence suggests that when people perceive that an is diagnostic but incorrect, they often attempt to adjust from that when formulating their estimate (Epley & Gilovich, 2001, 2005, 2006). For example, consider how people might respond if asked, Is the freezing point of vodka 32 1F? and then What is the freezing point of vodka? Although they know that the freezing point of vodka is not 32 1F, many people perceive that this is diagnostic because it is the freezing point of water. Hence, a downward adjustment from this is a legitimate strategy for making an educated guess at the answer to the second question. With respect to the second question, there are many factors that influence the amount of adjustment from a diagnostic. These factors include the perceived relevance of the to the judgment (Mussweiler & Strack, 1999), beliefs about the degree of error of the (Gilbert, 2002; Wegener & Petty, 1995), and the ambiguity and uncertainty associated with the (Einhorn & Hogarth, 1985). The common theme underlying all of these influences is that reduced confidence in the accuracy of a diagnostic will lead to a greater amount of adjustment. We believe that there is an additional, arguably more fundamental, factor that influences the amount of adjustment from a plausible. If adjustment is viewed as movement along a subjective representational scale, then the resolution of this scale might also influence the amount of adjustment. X units of adjustment along a fine-resolution scale will cover less objective distance than the same number of units of adjustment along a coarse-resolution scale. As a consequence, there will be less adjustment when numerical judgments are made using subjective scales with a finer resolution. Volume 19 Number 2 Copyright r 2008 Association for Psychological Science 121

2 Anchor Precision Influences the Amount of Adjustment EXPERIMENT 1 Experiment 1 assessed the influence of rounded versus precise s on the amount of adjustment from the. The precise s came in two forms. under s were values up to 3% below the rounded s. over s were values up to 3% above the rounded s. Table 1 lists the values of the rounded, precise under, and precise over s for the 10 scenarios used in this experiment. Forty-three students from an undergraduate subject pool participated in the experiment for extra credit. The experiment used a mixed design with type of (rounded, precise under, precise over) as a between-subjects factor and scenario (10 see Table 1) as a within-subjects factor. Respondents read the scenarios one at a time and provided a numerical estimate for each scenario before moving on to the next. Nine of the scenarios investigated price estimates (plasma TV, quick-melt cheese, beach house, pet rock, figurine) or estimates of attribute values (grams of protein in a health drink, pen life in kilometers, basketball shooting percentage, Hummer height). For example, the plasma-tv scenario stated: Imagine that you have just earned your first paycheck as a highly paid executive. As a result, you want to reward yourself by buying a large-screen, high-definition plasma TV. As you browse through a store, you see a plasma TV from Sony that you like because of its attractive carbon-fiber finish. Its WEGA 50-inch screen has been rated by a panel of electronics experts as the clearest and sharpest in the market today, because of a new technology that doubled its resolution and increased its contrast ratio to 4,000:1. If you were to guess the plasma TV s actual cost to the retailer (i.e., how much the store bought it for), what would it be? Because this is your first purchase of a plasma TV, you have very little information with which to base your estimate. All you know is that it should cost less than the retail price of $5,000/$4,988/$5,012. Guess the product s actual cost. This electronics store is known to offer a fair price. Most of their items are priced very close to their actual cost because they compete on volume. The only reason that this particular plasma TVis expensive is that it uses a new technology, and the picture quality is outstanding. So the actual cost would be only slightly less than $5,000/$4,988/$5,012. A context-free scenario (i.e., There is a number saved in a file on this computer. It is just slightly less than 10,000/9,989/ 10,011. Can you guess the number? ) was also included. We assumed this scenario was free of preexisting associations and that estimates would not be affected by inferences about the reliability of the. Main Analysis The raw cell means are reported in Table 1. The difference between the value and each estimate was calculated and transformed into a z score using the error term from the entire sample. The Type of Anchor Scenario interaction was not significant, F(18, 360) , so we collapsed the data across the 10 scenarios and found that the type of had a significant effect, F(2, 40) , o The rounded s (M , MSE 5 0.1) resulted in an adjustment that was larger than the average adjustment observed with the precise s (under: M , MSE ; over: M , MSE 5 TABLE 1 Anchor Values Used and Participants Mean Estimates in Experiment 1 Scenario Measure Rounded Anchor value under over Rounded Participants mean estimate under over Analysis of variance a F p rep Beach house Bid price ($) 800, , , , , , Beverage Protein (grams) Cheese Cost ($) Context-free Number 10,000 9,989 10,011 9,316 9,967 9, Basketball Field goal percentage Figurine Cost ($) Hummer Height (meters) Pen Life (kilometers) Pet rock Sale price ($) Plasma TV Cost ($) 5,000 4,998 5,012 4,158 4,569 4, Aggregate b a These columns present the results of analyses comparing estimates in the rounded- condition with the average estimates in the precise-under- and precise-over- conditions. b This row presents the average z scores across scenarios. 122 Volume 19 Number 2

3 Chris Janiszewski and Dan Uy 0.1), F(1, 40) , p rep 5.996, o The estimates did not differ between the precise under and precise over s, F(1, 40) Supplemental Analysis If different types of s induce people to represent their subjective scale differently, then rounded s should encourage rounded responses, and precise s should encourage precise responses. To test this idea, we coded each response for its level of precision. For example, in the beachhouse scenario, an estimate that was a multiple of $5,000, $10,000, or $25,000 was considered rounded. The rounded s resulted in a larger proportion of rounded responses (.73) than the precise under s (.49) and the precise over s (.46), F(1, 40) , p rep Discussion Experiment 1 shows that precise and rounded s result in estimates that are, respectively, closer to and farther from the value. We propose that the precision of an value can influence the resolution of the subjective scale used to represent the to-be-judged dimension. If respondents make an estimate by adjusting by X units on a subjective scale, they will cover less distance on a fine-resolution scale than on a coarseresolution scale. The results of Experiment 1 can be used to rule out two alternative hypotheses. First, it does not appear that the estimation process is based on the selective accessibility of information that results from considering the value. The rounded and precise s were similar in value, and therefore should have encouraged the consideration of similar information. Second, it does not appear that respondents took a proportion of the value to calculate their estimated value. If respondents were using a proportion rule, then the estimates associated with the rounded s should have been between the estimates associated with the precise under and precise over s. EXPERIMENT 2 A plausible alternative explanation for the results of Experiment 1 is that they were due to a difference in objective scale ranges. That is, a precise might evoke a narrower range of plausible responses than a rounded. If the adjustment from the value is a constant percentage change within the objective range of plausible responses, then the narrower range in the precise- condition would result in less adjustment than observed in the rounded- condition. In Experiment 2, we manipulated the objective scale range independently of precision. For example, the following information was added to the plasma-tv scenario in the broadrange condition (note that precise over s were not included in this experiment): You also know that electronics stores can make margins as high as 40%, suggesting that the cost could be as low as $3,000/$2,998, although these types of margins are usually for peripherals like headphones and/or ipod holders. In the narrow-range condition, a 20% margin was suggested in this scenario, and the possible actual cost was given as $4,000 or $3,998. If precision influences the resolution of the respondent s subjective scale, then the effect of precision on estimates would be independent of the effect of scale range. If precision influences the range of plausible objective values and not scale resolution, then the effect of precision either would be overwhelmed by the manipulation of scale range or would correlate with the observed effect of range. Eighty-five students from an undergraduate subject pool participated in this experiment for extra credit. The experiment used a mixed design with type of (rounded, precise under) and range of plausible values (narrow, broad) as betweensubjects factors and scenario (plasma TV, pet rock, beach house, Hummer, figurine) as a within-subjects factor. 1 The procedure mimicked that of Experiment 1 except for the addition of a manipulation check. After responding to all five scenarios, respondents reconsidered each scenario and provided a range of plausible estimates. To ensure that we would obtain a range effect, we set the lower values in the broad range to correspond to the lowest estimates reported in Experiment 1. The lower values in the narrow range were set to correspond to the median estimates in Experiment 1 (see Table 2). For both broad and narrow ranges, the lower values were precise when the was precise. Manipulation Check The plausible range values given by the participants were transformed into z scores. As expected, the range manipulation influenced the lowest plausible value. The lowest plausible value was lower in the broad-range condition (M , MSE 5 0.1) than in the narrow-range condition (M , MSE ), F(1, 81) , p rep 5.996, o There was no influence of the type of on the lowest plausible value, F(1, 81) , nor was there an interaction of range and type of, F(1, 81) As expected, the manipulations had no influence on the highest plausible value. Estimates As in Experiment 1, the difference between the value and each estimate was calculated and transformed into a z score. 1 The remaining scenarios could not be modified to be consistent with the range manipulation. Volume 19 Number 2 123

4 Anchor Precision Influences the Amount of Adjustment TABLE 2 Range of Values Presented in Experiment 2 Scenario Broad range Narrow range Rounded Rounded Beach house $700,000 $800,000 $699,800 $800,000 $750,000 $800,000 $749,800 $800,000 Figurine $25 $50 $24.50 $50 $35 $50 $34.50 $50 Hummer 2 m 2.3 m 1.98 m 2.3 m 2.1 m 2.3 m 2.08 m 2.3 m Pet rock $30 $40 $29.75 $40 $35 $40 $34.75 $40 Plasma TV $3,000 $5,000 $2,998 $5,000 $4,000 $5,000 $3,998 $5,000 The rounded s (M , MSE ) resulted in more adjustment than the precise s (M , MSE ), F(1, 81) , p rep 5.996, o The broad ranges (M , MSE ) resulted in more adjustment than the narrow ranges (M , MSE ), F(1, 81) , p rep 5.97, o There was no Range Type of Anchor interaction, F(1, 81) EXPERIMENT 3 Experiment 2 provides evidence that precision has an influence on adjustment that is independent of the influence of the objective range of plausible values. Experiment 3 addressed the possibility that precise s led to smaller adjustments because respondents perceived them as more accurate or valid (i.e., reliable) than rounded s. To test this hypothesis, we added a reliable-rounded- condition to the precise- and rounded- conditions. In the reliable-rounded- condition, information was added to the rounded- materials to make participants more confident in the. For example, the plasma-tv scenario was modified by adding, All you know are the following three things. First, the plasma TV should cost less than the retail price of $5,000. Second, you have checked the price of the plasma TVat three other stores in the area. They were all selling the plasma TV for $5,000. Third, you checked on-line and the lowest price you saw was $5,000. Similar modifications were made to the four other scenarios presented to participants (beach house, figurine, Hummer, pet rock). We expected that making an more reliable would lead to less adjustment. We also expected that the effect of the reliability manipulation would be independent of the effect of precision. If a reliable rounded is perceived as more reliable than a precise, but a precise results in less adjustment than a reliable rounded, then the reliability of the cannot be responsible for the precision effect. Forty-five students from an undergraduate subject pool participated in the experiment for extra credit. The experiment used a mixed design with type of (rounded, reliable rounded, precise under) as a between-subjects factor and scenario (plasma TV, pet rock, beach house, Hummer, figurine) as a within-subjects factor. The stimulus materials were identical to those used in Experiment 2 except for the additional information for the reliable rounded s. The procedure included checks on the manipulation of reliability. After responding to all five scenarios, respondents were asked to reconsider each scenario and indicate the reliability of the. They used three 7-point scales to indicate how informative they found the (not informative, very informative), how much they relied on it when making the estimate (not at all, considerably), and how confident they were that the was a good starting point for the estimate (not confident, very confident). Finally, participants were asked how much they tried to adjust from the. Manipulation Check The three measures of reliability were averaged to create a reliability index for each scenario (average Cronbach s a 5.86). The indices for the five scenarios were analyzed using a repeated measures multivariate analysis of variance. An initial analysis confirmed the effectiveness of the reliability manipulation, F(2, 42) , o Planned contrasts showed that the reliable rounded s (M , MSE ) were perceived as more reliable than the precise s (M , MSE ), F(1, 42) , p rep 5.996, o , but that the rounded s (M , MSE ) and precise s (M , MSE ) were perceived as equally reliable, F(1, 42) The degree to which participants perceived that they were trying to adjust from the did not vary by condition, F(2, 42) Estimates An initial analysis confirmed the influence of the manipulation, F(2, 42) , o The results of Experiment 1 were replicated: A planned contrast showed that the 124 Volume 19 Number 2

5 Chris Janiszewski and Dan Uy rounded s (M , MSE ) led to more adjustment than the precise s (M , MSE ), F(1, 42) , p rep 5.996, o Another planned contrast showed that the reliable rounded s (M , MSE ) led to more adjustment than the precise s (M , MSE ), F(1, 42) , p rep 5.996, o Thus, participants made larger adjustments from the reliable rounded s than from the precise s, even though they found the reliable rounded s to be more reliable than the precise s. We note that the reliability measures and estimate values differed between the rounded and reliable-rounded conditions. Thus, it is unlikely that the reliability scale had different representational properties across conditions (Birnbaum, 1999). EXPERIMENT 4 If rounded and precise s influence scale resolution, then estimates based on these s should diverge more as the number of units of adjustment increases. For example, suppose that a rounded evokes a subjective scale with units that are twice the width of those in a subjective scale evoked by a precise. Also suppose that the motivation to adjust influences the number of units of adjustment. As the motivation to adjust increases and the number of units of adjustment increases correspondingly, the amount of adjustment on the coarse-resolution scale should increase at a faster rate than the amount of adjustment on the fine-resolution scale (i.e., motivation to adjust and scale resolution should interact). Experiment 4 included two subexperiments in which motivation to adjust and width of the scale unit were manipulated between subjects. The high-motivation-to-adjust condition was created by removing information from the scenarios used in Experiment 2 (the scenarios from Experiment 2 were used without alteration in the low-motivation-to-adjust condition). For example, sentences in the plasma-tv scenario that encouraged a slight adjustment ( items are priced very close to their actual cost... actual cost would be only slightly less than $5,000 ) were replaced with a sentence that encouraged more adjustment ( What is your estimate of the TV s actual cost? ). Experiment 4a (n 5 59) manipulated the width of the scale unit by manipulating the precision of the (i.e., rounded for broad width and precise for narrow width). The remainder of the procedure mimicked the procedure in Experiment 1 (e.g., open-ended responses). Experiment 4b (n 5 149) manipulated width of the scale unit by replacing the open-ended response format with a demarcated line. The coarse-unit line had five numerically labeled hatch marks, and the fine-unit line had nine numerically labeled hatch marks. The endpoint labels and physical line lengths were identical across these conditions. The was always rounded. In Experiment 4a, there was a Motivation to Adjust Scale Unit Width interaction, F(1, 55) , p rep 5.947, o The difference in the amount of adjustment between the roundedand precise- conditions increased as the motivation to adjust went from low (M precise , M rounded , M difference ), F(1, 55) , p rep 5.994, o , to high (M precise , M rounded , M difference ), F(1, 55) , p rep 5.996, o In Experiment 4b, there was also a Motivation to Adjust Scale Unit Width interaction, F(1, 145) , p rep 5.882, o The difference in the amount of adjustment between the two response-line conditions increased as the motivation to adjust went from low (M fine , M coarse , M difference ), F(1, 145) , p rep 5.917, o , to high (M fine , M coarse , M difference ), F(1, 145) , p rep 5.99, o The symmetry of results across the two subexperiments suggests that the precision of an influences the resolution of the underlying subjective response scale. QUASI-EXPERIMENT 5 Real estate agents are sensitive to numerical s (Northcraft & Neale, 1987). We examined the possibility that home buyers exhibit similar behavior by analyzing 5 years of home sales data (N 5 25,564) from Alachua County, Florida. First, each list price was coded as being precise to the ten thousands, thousands, hundreds, tens, or ones. Discussions with brokers revealed that prices precise to the tens or ones (n 5 492) often indicate sales due to foreclosure; because such sales are not representative home sales, we excluded these data from our analysis. Second, the sales-price ratio (sale price/list price) was used to exclude sales that were completed at or above the list price, as these sales often involved a bidding war (n 5 12,491). The final sample included 12,581 homes priced between $600 and $2,000,000 (Mdn 5 $130,000). After we controlled for the list price, F(1, 12,577) , there was a main effect of list-price precision on the sales-price ratio, F(2, 12,577) , o There was a difference between the sales-price ratios for list prices that were precise to the hundreds (M , MSE ) and list prices that were precise to the thousands (M , MSE ), F(1, 12,577) , p rep 5.996, o ; there was also a difference between the sales-price ratios for list prices that were precise to the thousands and list prices that were precise to the ten thousands (M , MSE ), F(1, 12,577) , p rep 5.996, o An ancillary analysis showed that the difference between the amount of adjustment to a rounded versus a precise increased as the number of days Volume 19 Number 2 125

6 Anchor Precision Influences the Amount of Adjustment the home was listed on the market increased, F(2, 12,578) , o For example, the difference between the salesprice ratios for prices precise to the hundreds and prices precise to the ten thousands increased as the number of days the home was listed increased from less than 40 days (M 100s , M 10,000s , M difference ) to more than 100 days (M 100s , M 10,000s , M difference ). If the number of days a home is listed influences the buyer s motivation to adjust, then the effect of precision should increase as the number of days increases. GENERAL DISCUSSION The results of the five studies allow us to draw two conclusions, with different levels of confidence. First, a precise results in less adjustment than a rounded. The -precision effect is robust. It occurred with regularity across a large number of replicates, both inside the laboratory and in the field. Second, it appears plausible that precision influences resolution of the subjective scale, which in turn influences the amount that people adjust from an. This claim is more difficult to substantiate because the resolution of a subjective scale must be inferred from response patterns, and because there are other factors (e.g., objective scale range, confidence in the value) that also contribute to the amount of adjustment. There are also other adjustment strategies that might be used (e.g., proportion of the value). The -precision effect may be operative in a large number of real-world circumstances, influencing negotiations, assessments of health risk, and assessments of present and future value. For example, Galinsky and Mussweiler (2001) found that the initial offer in a negotiation acts as an, and hence has a significant influence on the settlement amount. Our results suggest that the influence of the initial offer will be stronger when the initial offer is precise, rather than rounded. Also, Michie, Lester, Pinto, and Marteau (2005) showed that patients are sensitive to the manner in which medical information is communicated. Patients seem to understand estimates of life expectancy and treatment responsiveness better when such information is presented in general terms (e.g., moderate risk, high risk ), rather than in specific terms (e.g., 40%, 80%; Brun & Teigen, 1988). Yet, to the extent that patients adjust initial estimates to account for family history, personal motivation, and other variables, general terms may encourage more adjustment and alter treatment choices. Anchor precision may also influence the confidence intervals people use to make decisions. Confidence intervals surrounding numerical values or estimates influence search for information, resource allocation, and willingness to execute a decision (Soll & Klayman, 2004). Yet, despite the importance of estimated confidence intervals, people are poor at generating them. For example, when people are asked to make an estimate and surround it with a 90% confidence interval, the interval includes the correct answer about 50% of the time, owing to the interval being too narrow (Klayman, Soll, González-Vallejo, & Barlas, 1999). One factor that may contribute to the narrowness of such confidence intervals is the resolution of the subjective scales used to generate the initial values (Soll & Klayman, 2004). If people begin the estimation process by generating an initial estimate, the precision of this initial estimate will influence the resolution of the subjective scale and the size of the confidence interval. Thus, policymakers should be able to increase the size of confidence intervals by encouraging people to generate a rounded initial estimate, and hence to use a coarse-resolution subjective scale. REFERENCES Birnbaum, M. (1999). 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7 Chris Janiszewski and Dan Uy Switzer, F.S., & Sniezek, J.A. (1991). Judgment processes in motivation: Anchoring and adjustment effects on judgment and behavior. Organizational Behavior and Human Decision Processes, 49, Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, Wegener, D.T., & Petty, R.E. (1995). Flexible correction processes in social judgment: The role of naïve theories in corrections for perceived bias. Journal of Personality and Social Psychology, 68, Wright, W.F., & Anderson, U. (1989). Effects of situation familiarity and financial incentives on use of the ing and adjustment heuristic for probability assessment. Organizational Behavior and Human Decision Processes, 44, (RECEIVED 2/15/07; REVISION ACCEPTED 6/29/07) Volume 19 Number 2 127